1. Cognitive Flexibility Theory Matt Koehler CEP 909 Nov 7, 2001

2. Why Non-linearity Not all domains require the use of potentially confusing non-linearity Simple domains are best left to simple presentation modes Reserve the use of non-linearity for “complex, ill-structured domains” [More in a bit about this] Propose Cognitive Flexibility Theory as a way to avoid the pitfalls of teaching and learning in an ill-structured domain

3. Complex, Ill-Structured? Domains that are not easily compartmentalized Domains that are not easy to understand Domains that require “deep understanding” between principles and practice Domains that require a lot of experience to learn well

4. Pitfalls to Avoid Singular representations -Students learn only one way to represent ideas (electricity is like water flowing through a pipe) Students over-simplify the domain (presenting a complex domain as a linear progression of ideas can make the domain seem simpler than it is). Compartmentalizing knowledge (seeing ideas in isolation). Presenting boundaries of learning (knowledge in complex domains is continual) Failing to understand the active process of learning Failure to transfer knowledge to new problems of practice

5. Cognitive Flexibility Theory to the rescue Represent knowledge in it’s smallest elements that still have meaning (e.g. “mini-cases”) Represent knowledge in multiple ways Never hide complexity from readers Mini-cases represent more than one idea, and represent the complex, ill-structured connections between multiple ideas Criss-cross the cases to produce flexible, rich understanding

6. Criss-Crossing the Conceptual Landscape “The best way to come to understand a given landscape is to explore it from many directions, to traverse it first this way and then that (preferably with a guide to highlight significant features). Our instructional system for presenting a complexly ill-structured “topical landscape” is analogous to a physical landscape exploration, with different routes of traversing study-sites (cases) that are each analyzed from a number of thematic perspectives” [Spiro et. al, 1987, pp-187]

7. Claimed Advantages of the Approach Students don’t: –Compartmentalize knowledge –Oversimplify –Rely on a few canonical cases Students do: –Develop multiple representations –Develop connections between knowledge –Are better able to transfer to new problems –Come away with a better overall understanding of complexity, multi-faceted knowledge, and learning (Mishra, et al) –Have accelerated learning experience

8. Remaining Questions? What counts as complex, ill-structured? How do you make a CFT hypertext? How would you go about proving any of these claims?